Problem: $J$ is the midpoint of $\overline{CT}$ C J T If: $ CJ = 3x - 7$ and $ JT = 5x - 25$ Find $CT$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {3x - 7} = {5x - 25}$ Solve for $x$ $ -2x = -18$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 3({9}) - 7$ $ JT = 5({9}) - 25$ $ CJ = 27 - 7$ $ JT = 45 - 25$ $ CJ = 20$ $ JT = 20$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {20} + {20}$ $ CT = 40$